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amcknight comments on Planets in the habitable zone, the Drake Equation, and the Great Filter - Less Wrong
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Maybe, but due to anthropic effects, this is one of the times in which we definitely cannot use the we're-not-special rule of thumb. Noting that we happen to have developed gives us absolutely no evidence about the rarity of observers that can notice that they've developed (except that it rules out theories that make it so rare that even 1 observer is unlikely).
Without more information about The Great Filter, most of the probability density does not reside in such perfectly balanced orders of magnitude (like 2% per 3Gyr-galaxy) to make us happen to be first. Though it's an open possibility that we're the first but not the only life that will develop, it's extremely unlikely that two huge numbers that could conceivably be orders of magnitude apart, happen to line up so closely.
I'm not sure I follow your last paragraph. What are the two huge numbers in this context?
The numbers I have in mind are something like: total number of planets and probability of any given planet to allow life to flourish across the galaxy. These numbers are independent. You could start with 'region of space' or involve time, but the numbers will still be independent. (i guess I should have said a huge and tiny number balancing when multiplied)